The Baku street event, scheduled for June 7th, becomes the eighth grand prix to be lost from the 2020 calendar as a result of the COVID-19 outbreak.
It joins Australia, Bahrain, Vietnam, China, the Netherlands, Spain and Monaco.
F1 is continuing to look for dates in which to slot postponed races later in the year, with only Monaco definitively cancelled for 2020.
In a statement, BCC said: "The postponement was agreed upon after extensive discussions with Formula 1 as well as the Federation Internationale de l'Automobile and the Government of the Azerbaijan Republic.
"This comes as a direct result of the ongoing global COVID-19 pandemic and has been based entirely on the expert guidance provided to us by the relevant authorities.
"In coming to this conclusion, BCC's primary concern throughout has been the health and well-being of the Azerbaijani people as well as all visiting F1 fans, staff and championship participants."
"BCC shares its fans disappointment at not being able to experience the pinnacle of motorsport race through the streets of Baku this June.
"To that end, we will continue to work closely with Formula 1, the FIA and the Government of the Azerbaijan Republic to monitor the situation with a view to announcing a new race date later in the 2020 season."
In theory, the earliest that the 2020 season can now start is with the Canadian GP in Montreal on June 14th, which was supposed to be the second of two back-to-back flyaway events.
However, a postponement seems likely to follow soon as Canada has been tightening restrictions. Overnight it became the first country to withdraw from the Tokyo Olympic Games, which starts in July.